How to make a Copper/Rose Gold smudge material?
I would just use a simple principled shade. 

Slide the metallic and specular (forgot to change specular) close to 1.

Choose a rose gold color and use a texture in your roughness. I put two options, a procedural way (noise texture stretched with mapping node) but I think an actual texture image looks better. 

Use an HDRI so you get more realistic reflections.